What is the Greatest Common Factor of 7575 and 7584?

Greatest common factor (GCF) of 7575 and 7584 is 3.

GCF(7575,7584) = 3

We will now calculate the prime factors of 7575 and 7584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7575 and 7584.

How to find the GCF of 7575 and 7584?

We will first find the prime factorization of 7575 and 7584. After we will calculate the factors of 7575 and 7584 and find the biggest common factor number .

Step-1: Prime Factorization of 7575

Prime factors of 7575 are 3, 5, 101. Prime factorization of 7575 in exponential form is:

7575 = 3¹ × 5² × 101¹

Step-2: Prime Factorization of 7584

Prime factors of 7584 are 2, 3, 79. Prime factorization of 7584 in exponential form is:

7584 = 2⁵ × 3¹ × 79¹

Step-3: Factors of 7575

List of positive integer factors of 7575 that divides 7575 without a remainder.

1, 3, 5, 15, 25, 75, 101, 303, 505, 1515, 2525

Step-4: Factors of 7584

List of positive integer factors of 7584 that divides 7575 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 79, 96, 158, 237, 316, 474, 632, 948, 1264, 1896, 2528, 3792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7575 and 7584. The biggest common factor number is the GCF number.
So the greatest common factor 7575 and 7584 is 3.

Also check out the Least Common Multiple of 7575 and 7584